Existence of optimal virtual element weights for mmWave FMCW MIMO radar based heart rate estimation

Measuring heart rate is a critical component of assessing cardiac health and detecting potential heart diseases at an early stage. Various sensors, including electrocardiogram and photoplethysmograph, are commonly employed for this purpose. However, these conventional methods necessitate direct contact with the patient's skin which may be impractical or uncomfortable in situations involving patients with skin diseases or burn injuries. To address these limitations, a concerted effort has been to develop non-contact methods leveraging frequency-modulated continuous-wave multiple-input multiple-output radar systems. Recent studies have illustrated the sensitivity of the phase component of received signals to micro-motion, presenting a promising avenue for effective heart rate estimation. However, existing literature predominantly focuses on single-antenna setups, overlooking the potential benefits offered by multiple-input multiple-output systems, which provide diverse channels with varying precision levels. This correspondence introduces a novel phase extraction model grounded in the argument of the analytic signal derived from both in-phase and quadrature channels. Furthermore, leveraging the normal equation, we establish the feasibility of optimizing weights assigned to individual virtual antennas to achieve a robust approximation of ground truth data. An I/Q signal phase term extraction model based on the the analytic signal is proposed. Via an optimization approach, the existence of the best weights for virtual antennas is demonstrated and pave the way for further research on new models for their estimation. image